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Convert the following Celsius temperatures to Fahrenheit: (a) \(-62.8^{\circ} \mathrm{C},\) the lowest temperature ever recorded in North America (February \(3,1947,\) Snag, Yukon); (b) \(56.7^{\circ} \mathrm{C},\) the highest temperature ever recorded in the United States (July \(10,1913,\) Death Valley, California); \((\mathrm{c}) 31.1^{\circ} \mathrm{C},\) the world's highest average annual temperature (Lugh Ferrandi, Somalia).

Short Answer

Expert verified
-62.8°C = -81.04°F, 56.7°C = 134.06°F, 31.1°C = 87.98°F.

Step by step solution

01

Understand the Conversion Formula

The formula to convert Celsius temperatures to Fahrenheit is given by:\[ F = \frac{9}{5}C + 32 \]where \( F \) is the temperature in Fahrenheit and \( C \) is the temperature in Celsius. We will use this formula to convert each Celsius temperature provided.
02

Convert -62.8°C to Fahrenheit

Using the conversion formula, substitute \( C = -62.8 \):\[F = \frac{9}{5}(-62.8) + 32 = (-113.04) + 32 = -81.04\]Thus, \(-62.8^{\circ}C\) is equivalent to \(-81.04^{\circ}F\).
03

Convert 56.7°C to Fahrenheit

Substitute \( C = 56.7 \) into the conversion formula:\[F = \frac{9}{5}(56.7) + 32 = 102.06 + 32 = 134.06\]Therefore, \(56.7^{\circ}C\) is equivalent to \(134.06^{\circ}F\).
04

Convert 31.1°C to Fahrenheit

Substitute \( C = 31.1 \) into the conversion formula:\[F = \frac{9}{5}(31.1) + 32 = 55.98 + 32 = 87.98\]Thus, \(31.1^{\circ}C\) is equivalent to \(87.98^{\circ}F\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Temperature Conversion
Temperature conversion between different units is a fundamental concept in science, particularly in physics and chemistry. It allows for a unified understanding and consistent communication of temperature readings across different regions and scientific disciplines.

The most commonly used formula for converting Celsius to Fahrenheit is
  • \[ F = \frac{9}{5}C + 32 \]
where \( F \) represents the temperature in Fahrenheit and \( C \) represents the temperature in Celsius.
This formula tells us how to transform a temperature value from the metric system to the imperial system. It's essential to memorize and understand how to apply it correctly, as it is frequently used.

Being able to convert between temperature scales is not just useful academically. It's also practical in real-life scenarios like travel, cooking, and weather predictions to accommodate different regional standards.
Fahrenheit
Fahrenheit is a temperature scale predominantly used in the United States and several other territories. Understanding this scale is crucial when dealing with international temperature readings.

The Fahrenheit scale was proposed by Daniel Gabriel Fahrenheit in 1724. In this system:
  • The freezing point of water is at \(32^{\circ}F\).
  • The boiling point of water is at \(212^{\circ}F\).
This places the freezing and boiling points of water exactly 180 degrees apart. This scale is particularly handy in meteorological contexts, providing a familiar measurement for residents of the U.S. born into this system.

When converting temperatures, understanding values like these helps to provide a better frame of reference, especially if you're transitioning from or reporting temperatures in Celsius.
Celsius
Celsius, originally known as centigrade, is the temperature scale most common in scientific contexts and everyday use outside of the United States. Developed by Swedish astronomer Anders Celsius in 1742, it simplifies many atmospheric and experimental conditions.

In the Celsius scale:
  • Water freezes at \(0^{\circ}C\).
  • Water boils at \(100^{\circ}C\).
This scale is extensively used in scientific research because it offers a straightforward division of the temperature between the two fixed points (freezing and boiling of water) into 100 equal intervals or degrees.

For international collaborations and publications, professionals should be comfortable working with Celsius to effectively communicate findings and understand the work of others in a globally accepted format.
Physics Problem-Solving
In physics, problem-solving often involves converting measurements to ensure accuracy and consistency in calculations.

Here's how you can effectively tackle temperature-related problems:
  • Understand the given: Always start by understanding what is being asked. Identify the temperatures you need to convert.
  • Use the correct formula: Apply the appropriate conversion formula. Transition between Celsius and Fahrenheit can be done using \( F = \frac{9}{5}C + 32 \).
  • Substitution: Substitute the Celsius value into the formula to find its equivalent in Fahrenheit, or vice versa.
  • Calculation: Carry out the mathematical operations step by step to avoid mistakes.
These steps embody the clear, detailed approach necessary in physics problem-solving. Having a logical and systematic method to solve these conversions ensures precision and boosts confidence when dealing with temperature data.

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Most popular questions from this chapter

"The Ship of the Desert." Camels require very little water because they are able to tolerate relatively large changes in their body temperature. While humans keep their body temperatures constant to within one or two Celsius degrees, a dehydrated camel permits its body temperature to drop to \(34.0^{\circ} \mathrm{C}\) overnight and rise to \(40.0^{\circ} \mathrm{C}\) during the day. To see how effective this mechanism is for saving water, calculate how many liters of water a \(400-\mathrm{kg}\) camel would have to drink if it attempted to keep its body temperature at a constant \(34.0^{\circ} \mathrm{C}\) by evaporation of sweat during the day (12 hours) instead of letting it rise to \(40.0^{\circ} \mathrm{C} .\) (Note: The specific heat of a camel or other mammal is about the same as that of a typical human, 3480 \(\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\) . The heat of vaporization of water at \(34^{\circ} \mathrm{C}\) is \(2.42 \times 10^{6} \mathrm{J} / \mathrm{kg}.\))

An insulated beaker with negligible mass contains 0.250 \(\mathrm{kg}\) of water at a temperature of \(75.0^{\circ} \mathrm{C}\) . How many kilograms of ice at a temperature of \(-20.0^{\circ} \mathrm{C}\) must be dropped into the water to make the final temperature of the system \(40.0^{\circ} \mathrm{C}\) ?

An aluminum tea kettle with mass 1.50 \(\mathrm{kg}\) and containing 1.80 \(\mathrm{kg}\) of water is placed on a stove. If no heat is lost to the surroundings, how much heat must be added to raise the temperature from \(20.0^{\circ} \mathrm{C}\) to \(85.0^{\circ} \mathrm{C}\) ?

You are making pesto for your pasta and have a cylindrical measuring cup 10.0 \(\mathrm{cm}\) high made of ordinary glass \(\left[\beta=2.7 \times 10^{-5}\left(\mathrm{C}^{\circ}\right)^{-1}\right]\) that is filled with olive oil \([\beta=6.8 \times\) \(10^{-4}\left(\mathrm{C}^{\circ}\right)^{-1} ]\) to a height of 2.00 \(\mathrm{mm}\) below the top of the cup. Initially, the cup and oil are at room temperature \(\left(22.0^{\circ} \mathrm{C}\right) .\) You get a phone call and forget about the olive oil, which you inadvertently leave on the hot stove. The cup and oil heat up slowly and have a common temperature. At what temperature will the olive oil start to spill out of the cup?

Why Do the Seasons Lag? In the northern hemisphere, June 21 (the summer solstice) is both the longest day of the year and the day on which the sun's rays strike the earth most vertically, hence delivering the greatest amount of heat to the surface. Yet the hottest summer weather usually occurs about a month or so later. Let us see why this is the case. Because of the large specific heat of water, the oceans are slower to warm up than the land (and also slower to cool off in winter). In addition to perusing pertinent information in the tables included in this book, it is useful to know that approximately two-thirds of the earth's surface is ocean composed of salt water having a specific heat of 3890 \(\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\) and that the oceans, on the average, are 4000 m deep. Typically, an average of 1050 \(\mathrm{W} / \mathrm{m}^{2}\) of solar energy falls on the earth's surface, and the oceans absorb essentially all of the light that strikes them. However, most of that light is absorbed in the upper 100 \(\mathrm{m}\) of the surface. Depths below that do not change temperature seasonally. Assume that the sunlight falls on the surface for only 12 hours per day and that the ocean retains all the heat it absorbs. What will be the rise in temperature of the upper 100 \(\mathrm{m}\) of the oceans during the month following the summer solstice? Does this seem to be large enough to be perceptible?

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